Solution of 3D contact shape optimization problems with Coulomb friction based on TFETI

被引：0
|
作者：
Alexandros Markopoulos
Petr Beremlijski
Oldřich Vlach
Marie Sadowská
机构：
[1] Safran Aircraft Engines,Department of Applied Mathematics
[2] VSB-Technical University of Ostrava,IT4Innovations National Supercomputing Center
[3] VSB-Technical University of Ostrava,undefined
来源：
Applications of Mathematics | 2023年 / 68卷
关键词：
shape optimization; nonsmooth optimization; contact problem; Coulomb’s friction; TFETI method; 65K10; 74M10; 65K05;
D O I：
暂无
中图分类号：
学科分类号：
摘要：
The present paper deals with the numerical solution of 3D shape optimization problems in frictional contact mechanics. Mathematical modelling of the Coulomb friction problem leads to an implicit variational inequality which can be written as a fixed point problem. Furthermore, it is known that the discretized problem is uniquely solvable for small coefficients of friction. Since the considered problem is nonsmooth, we exploit the generalized Mordukhovich’s differential calculus to compute the needed subgradient information.
引用
收藏
页码：405 / 424
页数：19
相关论文
共 50 条
  • [1] Solution of 3D contact shape optimization problems with Coulomb friction based on TFETI
    Markopoulos, Alexandros
    Beremlijski, Petr
    Vlach, Oldrich
    Sadowska, Marie
    [J]. APPLICATIONS OF MATHEMATICS, 2023, 68 (04) : 405 - 424
  • [2] A theoretically supported scalable TFETI algorithm for the solution of multibody 3D contact problems with friction
    Dostal, Z.
    Kozubek, T.
    Markopoulos, A.
    Brzobohaty, T.
    Vondrak, V.
    Horyl, P.
    [J]. COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING, 2012, 205 : 110 - 120
  • [3] Shape optimization in contact problems with Coulomb friction
    Beremlijski, P
    Haslinger, J
    Kocvara, M
    Outrata, J
    [J]. SIAM JOURNAL ON OPTIMIZATION, 2002, 13 (02) : 561 - 587
  • [4] SHAPE OPTIMIZATION IN CONTACT PROBLEMS WITH COULOMB FRICTION AND A SOLUTION-DEPENDENT FRICTION COEFFICIENT
    Beremlijski, P.
    Haslinger, J.
    Outrata, J. V.
    Patho, R.
    [J]. SIAM JOURNAL ON CONTROL AND OPTIMIZATION, 2014, 52 (05) : 3371 - 3400
  • [5] TBETI and TFETI Algorithms for Contact Shape Optimization Problems
    Vondrak, V.
    Kozubek, T.
    Sadowska, M.
    Dostal, Z.
    [J]. PROCEEDINGS OF THE SECOND INTERNATIONAL CONFERENCE ON PARALLEL, DISTRIBUTED, GRID AND CLOUD COMPUTING FOR ENGINEERING, 2011, 95
  • [6] Approximation and numerical realization of 3D contact problems with Coulomb friction and a solution-dependent coefficient of friction
    Ligursky, T.
    Haslinger, J.
    Kucera, R.
    [J]. INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, 2010, 82 (09) : 1180 - 1206
  • [7] An algorithm for the numerical realization of 3D contact problems with Coulomb friction
    Haslinger, J
    Kucera, R
    Dostál, Z
    [J]. JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, 2004, 164 : 387 - 408
  • [8] A Scalable TFETI Based Algorithm for 2D and 3D Frictionless Contact Problems
    Dostal, Zdenek
    Brzobohaty, Tomas
    Kozubek, Tomas
    Markopoulos, Alex
    Vondrak, Vit
    [J]. LARGE-SCALE SCIENTIFIC COMPUTING, 2010, 5910 : 92 - +
  • [9] SIGNORINI PROBLEM WITH COULOMB LAW OF FRICTION - SHAPE OPTIMIZATION IN CONTACT PROBLEMS
    HASLINGER, J
    [J]. INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, 1992, 34 (01) : 223 - 231
  • [10] Qualitative analysis of 3D elastostatic contact problems with orthotropic Coulomb friction and solution-dependent coefficients of friction
    Haslinger, Jaroslav
    Kucera, Radek
    Ligursky, Tomas
    [J]. JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, 2011, 235 (12) : 3464 - 3480
12345